(1) Field of the Invention
This invention generally relates to the analysis of fluid flow past an object and more particularly to a method and apparatus for predicting the characteristics of a fluid flowing past such an object.
(2) Description of the Prior Art
Understanding the characteristics of fluid as it flows past an object, such as an airfoil, is important both from the standpoint of understanding and improving the designs of such objects and in understanding the nature of any turbulence introduced as a result of relative motion of a fluid an airfoil, either by moving of the airfoil through the fluid or by moving the fluid past the airfoil.
In the past understandings of fluid flow have been derived from the observation of fluid flow past a model and by specific measurements. For example, U.S. Pat. No. 3,787,874 to Urban discloses a method for making boundary layer flow conditions visible by applying to the surface of a moving or stationary structural body to be exposed to the flow a reactive layer of at least one chemical color indicator, such as a cholesterinic liquid. The body is exposed to a flow of gas, such as air, which contains a reagent. The chemical color indicator can also be applied together with gelling means and a moisture binder. The chemical color indicator can also be absorbed by a high-contrast, absorbent paper which is then applied to the body. A metal or plastic foil coated with a binder and/or indicator can also be used for this purpose. A boundary layer flow pattern image is produced, which can subsequently be recorded.
U.S. Pat. No. 3,890,835 to Dotzer et al. discloses another approach to chemically recording flow patterns by treating the surface to form a reactive layer, entraining in the fluid a reagent compound which is capable of chemically changing the reactive layer, and then passing the fluid over the reactive layer which is to be examined. In this particular disclosure, a blade or other member of aluminum to be examined is treated to form a thin oxide film by anodic treatment. This film is impregnated with an organic dye. As an air stream containing a reactive substance passes over the treated blade, the acid vapors react with the dye and/or the oxide layer and produce a visible pattern upon the blade. This pattern is characteristic of the boundary layer flow of the air stream. An examination of the visible pattern helps to determine the proper design and operating characteristics of the blade.
U.S. Pat. No. 4,380,170 to Dotzer et al. discloses another process for chemically plotting the boundary layer flows over uncompacted, coated, anodically oxidized aluminum surfaces by using a colored or uncolored liquid or a coating or pointillization with a substance, preferably a dye, soluble in water or organic media and which can be included or adsorbed in the eloxal layer.
U.S. Pat. No. 4,727,751 discloses a mechanical sensor for determining cross flow vorticity characteristics. This sensor comprises cross flow sensors which are non-invasively adhered to a swept wing laminar surface either singularly, in multi-element strips, in polar patterns or orthogonal patterns. These cross flow sensors comprise hot-film sensor elements which operate as a constant temperature anemometer circuit to detect heat transfer rate changes. Accordingly, crossflow vorticity characteristics are determined via cross-correlation. In addition, the crossflow sensors have a thickness which does not exceed a minimum value in order to avoid contamination of downstream crossflow sensors.
These prior art approaches present visualizations or measurements that define certain aspects of the characteristics of fluid flow. However, they are designed primarily to determine characteristics at a boundary layer or some other localized site. Each requires the production of a physical model and physical testing of such models. Moreover, if the testing suggests any change to the shape of an airfoil, it is generally necessary to modify the physical model and run the tests again in order to validate any change. Such testing can become time-consuming and expensive to perform.
More recently, it has been proposed to utilize computer modeling techniques to produce such fluid flow analyses. Such computer modeling is attractive because it eliminates the need for physical models and holds the opportunity to reduce testing, particularly if design changes are made to an object undergoing test. Initially such techniques were applied to circular cylinders using a small number of discrete point vortices.
Eventually additional studies determined that vorticity was useful as a basis for understanding fluid flow. Vorticity is produced at a solid boundary because at the surface the fluid has no velocity (i.e., the fluid exhibits a no-slip condition). Once generated at the surface, vorticity diffuses into the volume of the fluid where it is advected by local flow. Conventional vortex methods generally mime this process. In accordance with such methods, the strengths of the vortex elements or segments originating on the body surface are determined by requiring that the velocity induced by all the vortex elements on the surface be equal and opposite to the velocity at the surface. It is assumed that this vorticity is contained in an infinitely thin sheet at the surface. In these methods a resulting matrix equation is solved for the surface vorticity at all points on the body simultaneously. Vorticity transfer to the flow is then accomplished by placing the vortex elements above the surface.
It has been recognized that these vortex methods have several shortcomings. When computational methods use point vortices in their simulations, mathematical singularities can produce divergent solutions. This has been overcome by using a kernel function that contains a regularized singularity. However, this kernel function depends in certain ad hoc assumptions such as the value of the cutoff velocity and core radius. While the no-slip and no-flow boundary conditions provide information regarding the strength of the surface vorticity and subsequent strength of the vortex element, their use often neglects the effects of all other vortex sheets on the surface. Other implementations of such methods neglect the effects of coupling between the surface vortex sheets and surface sources. Finally, many methods assume a priori a separation point to analyze shedding of vorticity from the surface into the flow that generally requires experimental knowledge of the flow.
More recent prior art has utilized computer modeling based upon the nature of vortex elements at the surface of an object, such as an airfoil. These models then track the motion of each element as it moves into the flow over time to calculate the velocity of each element. While this prior art produces acceptable results, the direct calculation of the velocity of each vortex element produces an N.sup.2 increase in the required time for processing where N is the number of vortex elements for each time step. Such increases can become unacceptable when high resolution demands the calculation of a large number of vortex elements.